Dissipative linear response in a fermion system

K. Gütter, P.‐G. Reinhard, K. Wagner +1 more

Arnold J. Glick

Rhys Matt Andrew Anderson

In this thesis, we observe and characterize the current response of neutral fermions to a periodic applied force, thereby obtaining their conductivity. The experiment takes place in a 3D optical lattice subject to weak harmonic confinement, where a quantum gas microscope enables high-resolution fluorescence imaging of atoms pinned to lattice sites. Using micron-scale periodic displacements of an underlying harmonic potential to provide the oscillating uniform force, we measure the global current response of the atoms up to frequencies sufficient to characterize intraband transport, but well below the bandgap. We observe that the current response scales linearly with the forcing, providing experimental verification that data is taken in the linear response regime. The resulting conductivity spectra are analyzed and fit using five different models, from which a broadening parameter and the spectral weight of the response may be obtained. Broadening of the current response spectrum provides a measure of the rate of dissipation, and increases with lattice depth, interaction strength, and density. This dissipation occurs purely due to fermion-fermion collisions, given the absence of phonons or impurities in our potentials. It is observed to require a finite lattice depth in order to break Galilean invariance, as well as to enable Umklapp scattering events, which play a significant role in the dynamics. Measured dissipation rates collapse onto the predictions of a kinetic theory under the wide range of conditions studied. The spectral weight of the conductivity spectrum predicts the impulse response of the global current. It satisfies a sum rule in the limit of small lattice depth, but diminishes as the depth increases, reflecting an increase in the band-averaged effective mass. Measured under varying temperatures, densities, interaction strengths, and lattice depths, the spectral weight is shown to collapse onto the predictions of a thermodynamic description of the system. Furthermore, it is shown to be unaffected by varying the strength of interactions between the fermions, illustrating a fundamental prediction for conductivity spectra. As our measurements approach a high-temperature regime, the inverse of the spectral weight is shown to approach T-linear behaviour.

Lei Pan

Linear response theory is the theoretical foundation of modern experiments. In particular, it plays a vital role in measuring quantum matters. Its main idea is to take the external probe signal of the physical system as a perturbation and use the correlation function in the unperturbed equilibrium state to depict the response to the observable in system. In recent half century, the linear response theory for the closed quantum system has achieved great success in experiments on quantum matters. In recent years, with the tremendous progress of the precise manipulation of the light-matter interaction, the ultracold atom experiments can precisely control dissipative quantum many-body systems. With the discovery of many novel phenomena, dissipative quantum systems and non-Hermitian physics have attracted extensive attention in theory and experiment. We developed a linear response theory, named non-Hermitian linear response theory, to deal with open quantum systems. This theory takes the non-Hermitian term and quantum noise, which are induced by dissipation, as an external perturbative input, to detect the properties of the quantum system, and relates the time evolution of the observable with the correlation function in the unperturbed state of the system. The non-Hermitian linear response theory provides a new method for distinguishing the exotic quantum phase from the normal phase. The theoretical predictions are highly consistent with the recent experimental results of cold atom systems. This paper will review the non-Hermitian linear response theory and discuss its applications in quantum many-body and time-reversal symmetric quantum systems.

Vincenzo Branchina, Marco Fedele Di Liberto, Ivano Lodato

The fluctuation-dissipation theorem (FDT) is very general and applies to a broad variety of different physical phenomena in condensed matter physics. With the help of the FDT and following the famous work of Caldeira and Leggett, we show that, whenever linear response theory applies, any generic bosonic or fermionic system at finite temperature T can be mapped onto a fictitious system of free-harmonic oscillators. To the best of our knowledge, this is the first time that such a mapping is explicitly worked out. This finding provides further theoretical support to the phenomenological harmonic oscillator models commonly used in condensed matter. Moreover, our result helps in clarifying an interpretation issue related to the presence and physical origin of the Bose-Einstein factor in the FDT.